Satoshi Nakamura (EBAC, JLab)
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1 Extraction of P 11 resonances from πn data and its stability (arxiv:11.583) Satoshi Nakamura (EBAC, JLab) EBAC Collaborators H. Kamano (JLab) T. S.-H. Lee (ANL) T. Sato (Osaka U.)
2 Introduction Extraction of N from πn data is important! Understanding spectrum and structure of N within QCD Steps to extract N 1. Construct a reaction model through analysis of data 2. From the constructed model, resonance properties (pole position, vertex form factor) are extracted with analytic continuation
3 Extraction of N properties is inevitably model-dependent! Several different approaches : EBAC, GWU/VPI, Jülich and more Existence of some N is controversial Question! How much extracted N parameters depend on 1. model 2. precision of data
4 What we study (I) Stability of pole structure of the Roper resonance [N 11 (144)] against Large variation of parameters of EBAC-DCC model Including bare nucleon state Variation of P 11 amplitude for 1.6 < W < 2 GeV (II) Dependence of higher mass P 11 resonances on these variations (III) Stability of residues of the poles
5 Model and Method EBAC-DCC (Dynamical Coupled-Channel) model Matsuyama et al., Phys. Rep. 439, 193 (27) Lippmann-Schwinger equation T ab = V ab + c V ac G c T cb {a, b, c} = γ ( ) N, πn, ηn, ππn(π, σn, ρn) KΛ, KΣ, ωn V ab = v ab + N Γ N,a Γ N,b E m N
6 Bare Nucleon Model Pearce and Afnan, PRC 34, 991 (1986) Potentials V ab = v ab + Γ N,a Γ N,b E m N + N Γ N,a Γ N,b E m N v - v = Nucleon Pole Condition M B N M B (i) (ii) T (E m N ) Γ = F phys πnn Γ Γ E m N
7 Extraction of N information with analytic continuation πn scattering amplitude near a pole (E M R ) Suzuki et al., PRC 79, 2525 (29) F πn (E) Γ (M R ) Γ (M R ) E M R + (regular terms) Parameters characterizing Resonance Pole position of amplitude : M R N MB decay vertex : Γ (M R )
8 Multi-layered structure of scattering amplitudes e.g., single-channel meson-baryon scattering T (p, p; E) = V (p, p) + dqq 2 V (p, q) G(q, E) T (q, p; E) Scattering amplitude is a double-valued function of E! physical sheet unphysical sheet Im (E) X E th (branch point) X E th (branch point) Re (E)
9 Multi-layered structure of scattering amplitudes e.g., single-channel meson-baryon scattering T (p, p; E) = V (p, p) + dqq 2 V (p, q) G(q, E) T (q, p; E) Scattering amplitude is a double-valued function of E! physical sheet unphysical sheet Im (E) X E th (branch point) X E th (branch point) Re (E)
10 Multi-layered structure of scattering amplitudes e.g., single-channel meson-baryon scattering T (p, p; E) = V (p, p) + dqq 2 V (p, q) G(q, E) T (q, p; E) Scattering amplitude is a double-valued function of E! physical sheet unphysical sheet Im (E) X E th (branch point) X E th (branch point) Re (E)
11 Multi-layered structure of scattering amplitudes e.g., single-channel meson-baryon scattering T (p, p; E) = V (p, p) + dqq 2 V (p, q) G(q, E) T (q, p; E) Scattering amplitude is a double-valued function of E! C physical sheet unphysical sheet Im (E) X E th (branch point) X E th (branch point) Re (E)
12 Results 1 : Stability of pole positions Benchmarks (single energy solution) (SP6) = Parameters of all models are fitted SAID EDS (energy-dependent solution) (SP6) (Julía-Díaz et al., PRC 76, 6521 (27) )
13 P 11 amplitude.3.2 SAID EDS Re A.1 Im A SAID EDS Model upuupp upuppp uuuuup χ 2 pd SAID-EDS(SP6) (1359, 81) (1388, 83) 2.94 (1357, 76) (1364, 15) (182, 248) 3.55
14 P 11 amplitude.3.2 SAID EDS Re A.1 Im A Pole positions (s πn, s ηn, s ππn, s π, s ρn, s σn ) = (u, p, u, u, p, p).2.1 SAID EDS
15 More Models 1 2N -3p v v smooth fit 2N -4p v v fitted to oscillated behavior Re A.3 2N*-3p 2N*-4p Im A N*-3p.2 2N*-4p
16 Re A.3 2N*-3p 2N*-4p Im A N*-3p.2 2N*-4p Model upuupp upuppp uuuupp uuuuup χ 2 pd SAID-EDS(SP6) (1359, 81) (1388, 83) 2.94 (1357, 76) (1364, 15) (182, 248) N -3p (1368, 82) (1375, 11) (181, 82) N -4p (137, 81) (1384, 115) (1635, 68) (196, 214) 3.36 Roper two poles are stable! Additional pole in 2N 4p! Different high W amplitude Different higher mass pole position
17 More Models 2 (Bare Nucleon Model).3.2 Bare-N Re A Im A.3 Bare-N Model upuupp upuppp uuuupp uuuuup χ 2 pd SAID-EDS(SP6) (1359, 81) (1388, 83) 2.94 (1357, 76) (1364, 15) (182, 248) N 1N -3p (1364, 81) (1377, 129) (1769, 132) 2.51 Roper two poles are stable!
18 Different data SAID-SES for W 1.55 GeV CMB for W 1.55 GeV Re A CMB-fit SAID-CMB Im A CBM-fit.1 SAID-CMB
19 Re A CMB-fit SAID-CMB Im A CBM-fit.1 SAID-CMB Model upuupp upuppp uuuupp uuuuup χ 2 pd SAID-EDS(SP6) (1359, 81) (1388, 83) 2.94 (1357, 76) (1364, 15) (182, 248) N -4p-CMB (1379, 89) (1386, 19) (1613, 42) (1913, 324) 4.91 Roper two poles are stable!
20 Results 2 : Residues πn scattering amplitude F πn (E) E Epole (kinematical factor) Γ (E pole ) Γ (E pole ) E E pole = R e iφ E E pole [R, φ(deg.)] upuuupp upuppp uuuuup [37, 111] [64, 99] [2, 169] 2N -3p [44, 95] [75, 98] [4, 128] 1N -1N -3p [41, 18] [88, 11] [18, 155] Residue is more sensitive to details of amplitude!
21 Summary 1 Roper two poles are stable against Large variation of parameters within EBAC-DCC (v v ) Inclusion of bare nucleon state Fitting to different amplitude provided amplitudes are precisely fitted to for W < 1.5 GeV Average and range of Roper pole positions E pole = i (s π = u), i (s π = p)
22 Higher mass resonance pole exists in our models Rather model-dependent position : E pole = i It doesn t exist in SAID EDS = need for simultaneous fit to inelastic channel (πn ηn) S. Ceci et al., PRL 97, 622 (26) Possible pole in W 1.6 GeV (caused by oscillatory amplitude) = need for more precise πn data Residue for P 11 seems more sensitive to details of amplitude Simultaneous fit to inelastic channels
Stability of P 11 Resonances Extracted from πn data. Satoshi Nakamura. [Phys. Rev. C 81, (2010)] (Excited Baryon Analysis Center, JLab)
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